gen-define-the-pythagorean-expectation-and-give-one-short-worked-ead3

Define the Pythagorean expectation and give one short worked example.

# Pythagorean Expectation **Pythagorean expectation** is a formula used in baseball (and adapted to other sports) to estimate a team's winning percentage based on runs scored and runs allowed. ## Formula $$\text{Win\%} = \frac{\text{Runs Scored}^2}{\text{Runs Scored}^2 + \text{Runs Allowed}^2}$$ The exponent is often refined to ~1.83 for better accuracy in baseball, but 2 is the traditional value (hence "Pythagorean"). ## Worked Example Suppose a baseball team has: - **Runs Scored**: 800 - **Runs Allowed**: 700 $$\text{Win\%} = \frac{800^2}{800^2 + 700^2} = \frac{640,000}{640,000 + 490,000} = \frac{640,000}{1,130,000} ≈ 0.566$$ **Expected winning percentage: 56.6%** Over a 162-game season, this predicts approximately **0.566 × 162 ≈ 92 wins**. This helps identify teams that may be over- or under-performing relative to their run differential.